Direct and inverse problems of the ray tomography on the creeping waves

Ray tomography widely applied in the global seismology, exploration geophysics and seismic engineering usually uses body waves. Surface waves are employed rarely, partly because of their more complicated cinematic and dynamical properties. However, it is possible to point out problems whose effective solution can be gained only by surface wave ray tomography. In the paper we consider, by means of numerical modeling, the time inversion of creeping spiral waves. These waves are able to transit along the curved interface for a long distance reaching the shadow. The essential feature of the problem is in the existence of the velocity dependence on the local interface curvature. As it result, an effect just the same as anisotropy, appears. Thus, we are facing a 2D inversion problem for the anisotropic medium. The short wave approximation for the spiral wave velocities, as functions of the interface curvature and frequency, were given in Krauklis (1974). We use this approximation to consider both the direct and the inverse problem. For the time inversion, the method based upon the Tichonov regularisation (Ryzhikov and Troyan 1994) is applied here. From our point of view it affords to take the a priori information into consideration in the most natural way. To avoid the computational difficulties caused by a singularity in the solution, we use a suboptimal procedure.